Preheat the oven to 350 degrees Fahrenheit.
Place the butter into a 9x9 baking pan and place the pan into the oven while it preheats so the butter melts completely.
In a bowl, mix together the self-rising flour, sugar, and milk until smooth.
Carefully pour the batter mixture into the melted butter without stirring.
Spoon the fruit evenly over the batter, including syrup or juices if using canned fruit or pie filling.
Sprinkle cinnamon sugar over the top if desired.
Bake for 30 to 45 minutes until the crust is golden brown and the center is fully cooked through.
Allow the cobbler to cool for about 10 minutes before serving.